Download Unit 1 Student Edition

Unit 1.1 – Basic Properties of Exponents
Student Learning Targets:
 I can understand the properties of exponents and how to use them.
 I can simplify algebraic terms with common base exponents.
Properties of exponents
An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written
like this: 23) means:
2 x 2 x 2 = 8
Referring to 23, 2 is called the Base and 3 is called the exponent.
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Secondary Math II
Notes(1.1):
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Secondary Math II
Assignment 1.1
Evaluate using the properties of exponents.
1. 33 ∙ 32
3.
5.
2. (4−2 )3
52
3 4
4. ( )
55
5
34
2 −5 2 4
6. ( )
3−2
3
(3)
Simplify the expression.
7. (22 𝑦 3 )5
8. (3𝑎3 𝑏 5 )−3
9. (𝑤 3 𝑥 −2 )(𝑤 6 𝑥 −1 )
10. (5𝑠 −2 𝑡 4 )−3
11.
13.
𝑤 −2
12.
𝑤6
𝑥 2 𝑦 −3
3𝑦 2
∙
𝑦2
14.
𝑥 −4
-- 3 --
3𝑐 3 𝑑
9𝑐𝑑 −1
𝑥 −1 𝑦 2
𝑥 2 𝑦 −1
Secondary Math II
Unit 1.2 – Use the Properties of Rational and Irrational Numbers
Student Learning Targets:
 I can simplify radical expressions.
 I can add, subtract, and multiply real numbers
 I can explain why adding and multiplying two rational numbers results in a rational number.
 I can explain why adding a rational number to an irrational number results in an irrational number.
 I can explain why multiplying a nonzero number to an irrational number results in an irrational
number.
A rational number can be written as a terminating or repeating decimal. Irrational numbers are nonterminating, non-repeating decimals.
Notes:
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Secondary Math II
Notes (Continued for 1.2):
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Secondary Math II
Assignment 1.2
Simplify each radical expression.
1. √125
2. √50
3. √200
4. √−162𝑥 2 𝑦 3
5. √108𝑥 3 𝑦
6. √27𝑥 5 𝑦 7
3
3
Find each sum or difference.
4
8. −3√3 + 3√3 + 2√3
7. 2√5 − 5√3 − 2√3
4
4
3
4
3
9. 4√10 − √10 − 2 √10
10. 6√3 − 7√5 + 2√5 − 2√3
11. 3√8 + 4√16 − √2 + 5
12. 6√9 + 2√20 − 3√5 − √25
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Secondary Math II
Assignment 1.2 (Continued)
Find each product. Simplify each expression fully.
13. √10(√6 + √10)
14. √3(4√6 + 5)
15. √5(3√10 + 4)
16. √6(2 + 3√2)
4
4
17. (−2√3 + 5)(4√3 + 4)
3
3
3
18. (1 + √2)(−3 − 2√2)
3
19. ( √2 + √5)( √2 − √5)
Additional Problems:
20. (√2 + 3√5)(√2 − 3√5)
UM2: Page 248 #17-34; Page 254 #1-25
MA2: Page 424 #32-40, 52-55
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Secondary Math II
Unit 1.3 – Extend the Properties of Exponents to Rational Exponents
Student Learning Targets:
 I can convert radical notation to rational exponent notation, and vice-versa.
 I can extend the properties of integer exponents to rational exponents and use them to simplify
expressions.
𝑛
𝐿𝑒𝑡 𝑎1⁄𝑛 𝑏𝑒 𝑡ℎ𝑒 𝑛𝑡ℎ 𝑟𝑜𝑜𝑡 𝑜𝑓 𝑎, 𝑎𝑛𝑑 𝑙𝑒𝑡 𝑚 𝑏𝑒 𝑎 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟, 𝑡ℎ𝑒𝑛 ( √𝑎)
𝑚
𝑚
= (𝑎1⁄𝑛 ) = 𝑎𝑚⁄𝑛
Notes:
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Secondary Math II
Notes (continued for 1.3):
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Secondary Math II
Assignment 1.3
Write each expression in radical form.
1. 83⁄5
2. 197⁄2
3. 𝑥 1⁄4
Write each expression in exponential form.
3
4. ( √4)
5
7
5. ( √𝑤 )
6
6. √5
Simplify each expression using the properties of rational exponents.
8. (61⁄2 ∗ 41⁄4 )2
7. 71⁄4 ∗ 71⁄2
10.
5
421⁄3
2
11. ( 61⁄3 )
4
√5
2𝑥 5
3⁄4
𝑎−3⁄2 𝑏 3⁄2 𝑎1⁄2 𝑏2
𝑎1⁄3 𝑏 1⁄2
12. (125𝑥 −6 )1⁄3
𝑥 3⁄2 𝑦 −9⁄2
5
15. ( √2𝑥 4 𝑦 3 )−10
14. 𝑥 5⁄2 𝑦 7⁄2 𝑥 −7⁄2
13. (32𝑥 25 )
16. (
9. (45 ∗ 35 )−1⁄5
4
)
2
4
17. (√𝑤 7/4 𝑦16 𝑟 12 𝑤 −3/4 )
6
18
18. (𝑎3/2 𝑏 5/3 ) (𝑏𝑎7/9 )
Additional Problems: MA2: Page 417 #7-14, 21-32; Page 425 #3-22
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Secondary Math II
Unit 1.4 – Perform Arithmetic Operations with Complex Numbers
Student Learning Targets:
 I can understand that the set of complex numbers includes the set of all real numbers and the set
of imaginary numbers.
 I can express numbers in the form a + bi.
 I can add, subtract, and multiply complex numbers.
A complex number is any number in the form a + bi. The imaginary unit i is defined as 𝑖 = √−1. We
commonly use the fact i2 = –1 to help us in simplifying expressions.
Notes:
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Secondary Math II
Notes (Continued for 1.4):
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Secondary Math II
Assignment 1.4
Simplify.
1. √−121
2. √−169
3. √−32
4. √−162
Write the expression as a complex number in standard form.
5. √−81 + √16
6. √−144 + √121
7. √−180 + √98
8. √−75 + √288
Write the expression as a complex number in standard form.
9. (6 − 3𝑖) + (5 + 4𝑖)
10. (−1 + 4𝑖) + (−9 − 2𝑖)
11. (−14𝑖 − 3) + (−7𝑖 + 6)
12. (4𝑖 − 10) + (7 − 8𝑖)
13. (−2 − 6𝑖) − (4 − 6𝑖)
14. (−1 + 𝑖) − (7 − 5𝑖)
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Secondary Math II
Assignment 1.4 (Continued)
15. (6𝑖 + 4) − (10𝑖 + 8)
16. (3𝑖 − 8) − (11 + 7𝑖)
17. 6𝑖(3 + 2𝑖)
18. −2𝑖(−7𝑖 + 14)
19. 𝑖(4 − 10𝑖)
20. (8 − 3𝑖)(2 + 4𝑖)
21. (3 + 2𝑖)(−2 − 3𝑖)
22. (−2 − 𝑖)(11 + 6𝑖)
23. (2 + 2𝑖)(2 − 2𝑖)
24. (−5 − 3𝑖)(−5 + 3𝑖)
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Secondary Math II